Prove that n⁷ +7 is never a perfect square.
This proof used parity, binomial expansion, quadratic residues and the fact of the sum of squares. The main( last) fact was that if the product of two coprime odd numbers is equal to the sum of two squares, then the non square parts of the integers are congruent to 1mod4.
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Find all positive integer n
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Prove that n^3 +11n is divisible by 6
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Solving a cubic equation using Cardano's formula
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Find all n greater than 1 such that (2^n + 1)/n^2 is an integer.
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e Was Hiding Something — Hermite Finally Caught It
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Find all prime pairs (p, q) such that p^3 - q^7 = p - q
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A fun proof for an integer
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this limit has a dangerous solution!!
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Find the minimum a + b + c + d
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6 Impossible Puzzles With Surprising Solutions
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Prove that the nested radical is less than 2 for all n
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Find all pairs (x, p)
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When Math Isn’t Based in Reality
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if x+y=8, find the max of x^y (Lambert W function)
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Prove that this difference of squares is a multiple of 48
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If You Have A Bad Memory, I’ll Help You Fix It In 28 Minutes
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Can Sine be Factored?
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2 Circles, 1 Square – Can YOU Find The Area?
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'Hardest' IMO question of 1988 (#6)
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